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On solutions set of a multivalued stochastic differential equation

Marek T. MalinowskiRavi P. Agarwal — 2017

Czechoslovak Mathematical Journal

We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.

Extended Riemann-Liouville type fractional derivative operator with applications

P. AgarwalJuan J. NietoM.-J. Luo — 2017

Open Mathematics

The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.

Periodicity, almost periodicity for time scales and related functions

Chao WangRavi P. AgarwalDonal O’Regan — 2016

Nonautonomous Dynamical Systems

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

Solution to Fredholm integral inclusions via ( F, δ b )-contractions

Hemant Kumar NashineRavi P. AgarwalZoran Kadelburg — 2016

Open Mathematics

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

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